Q: What is the prime factorization of the number 36,025,344?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 1,303
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 1,303 }
  • Written in exponential form: 210 x 33 x 1,3031

Why is the prime factorization of 36,025,344 written as 210 x 33 x 1,3031?

What is prime factorization?

Prime factorization or prime factor decomposition is the process of finding which prime numbers can be multiplied together to make the original number.

Finding the prime factors of 36,025,344

To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.

If it doesn't make sense yet, let's try it...

Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 36,025,344 by 2

36,025,344 ÷ 2 = 18,012,672 - No remainder! 2 is one of the factors!
18,012,672 ÷ 2 = 9,006,336 - No remainder! 2 is one of the factors!
9,006,336 ÷ 2 = 4,503,168 - No remainder! 2 is one of the factors!
4,503,168 ÷ 2 = 2,251,584 - No remainder! 2 is one of the factors!
2,251,584 ÷ 2 = 1,125,792 - No remainder! 2 is one of the factors!
1,125,792 ÷ 2 = 562,896 - No remainder! 2 is one of the factors!
562,896 ÷ 2 = 281,448 - No remainder! 2 is one of the factors!
281,448 ÷ 2 = 140,724 - No remainder! 2 is one of the factors!
140,724 ÷ 2 = 70,362 - No remainder! 2 is one of the factors!
70,362 ÷ 2 = 35,181 - No remainder! 2 is one of the factors!
35,181 ÷ 2 = 17,590.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
35,181 ÷ 3 = 11,727 - No remainder! 3 is one of the factors!
11,727 ÷ 3 = 3,909 - No remainder! 3 is one of the factors!
3,909 ÷ 3 = 1,303 - No remainder! 3 is one of the factors!
1,303 ÷ 3 = 434.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
1,303 ÷ 5 = 260.6 - This has a remainder. 5 is not a factor.
1,303 ÷ 7 = 186.1429 - This has a remainder. 7 is not a factor.
1,303 ÷ 11 = 118.4545 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
1,303 ÷ 1,303 = 1 - No remainder! 1,303 is one of the factors!

The orange divisor(s) above are the prime factors of the number 36,025,344. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 1,303 = 36,025,344. It can also be written in exponential form as 210 x 33 x 1,3031.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 36,025,344.

36,025,344
Factor Arrows
218,012,672
Factor Arrows
29,006,336
Factor Arrows
24,503,168
Factor Arrows
22,251,584
Factor Arrows
21,125,792
Factor Arrows
2562,896
Factor Arrows
2281,448
Factor Arrows
2140,724
Factor Arrows
270,362
Factor Arrows
235,181
Factor Arrows
311,727
Factor Arrows
33,909
Factor Arrows
31,303

More Prime Factorization Examples

36,025,34236,025,34336,025,34536,025,346
21 x 18,012,6711791 x 5931 x 769151 x 7,205,069121 x 71 x 171 x 371 x 4,0911

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